TY - JOUR
T1 - A canonical construction for nonnegative integral matrices with given line sums
AU - Fernandes, Maria do Rosário Silva Franco
AU - F. da Cruz, Henrique
N1 - Foundation for Science and Technology (UID/MAT/00212/2013)
PY - 2015
Y1 - 2015
N2 - Let p be a positive integer and let A((p)) (R, S) be the class of nonnegative integral matrices with entries less than or equal to p, with row-sum partition R, and column-sum partition S. In this paper we state a new necessary and sufficient condition for A((p)) (R, S) not equal empty set. This condition generalizes the well known Gale-Ryser theorem. We also present a canonical construction for matrices in A((p)) (R, S).
AB - Let p be a positive integer and let A((p)) (R, S) be the class of nonnegative integral matrices with entries less than or equal to p, with row-sum partition R, and column-sum partition S. In this paper we state a new necessary and sufficient condition for A((p)) (R, S) not equal empty set. This condition generalizes the well known Gale-Ryser theorem. We also present a canonical construction for matrices in A((p)) (R, S).
KW - Algorithm
KW - Integral matrices with given lines
KW - Partition domination
U2 - 10.1016/j.laa.2015.06.033
DO - 10.1016/j.laa.2015.06.033
M3 - Article
VL - 484
SP - 304
EP - 321
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
SN - 0024-3795
ER -